You're correct, a direct migration of data between the 2 platforms is not possible.
The only option you have here if the source data is no longer available, is a convoluted process of exporting your data to csv and importing it again into your new instance. There's a Community article here that talks about how to do this when you want to update the actual indexed data, but the same principle can be applied to your use case.
Please note that if you need help in migrating your data, that would fall under the Professional Services banner, as it is rarely a straightforward task and there are always local environment factors to consider.
If all you want is that your data remains available for searching when you spin up your new Linux instance, then it may be easier for you to leave your old Sparc instance in place and configured distributed searching so that it will be searchable from the new instance.
